Geodesic
Bonferroni-Galambos inequalities for partition lattices
The electronic journal of combinatorics, Tome 11 (2004) no. 1
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In this paper, we establish a new analogue of the classical Bonferroni inequalities and their improvements by Galambos for sums of type $\sum_{\pi\in {\Bbb P}(U)} (-1)^{|\pi|-1} (|\pi|-1)! f(\pi)$ where $U$ is a finite set, ${\Bbb P}(U)$ is the partition lattice of $U$ and $f:{\Bbb P}(U)\rightarrow{\Bbb R}$ is some suitable non-negative function. Applications of this new analogue are given to counting connected $k$-uniform hypergraphs, network reliability, and cumulants.
DOI : 10.37236/1838
Classification : 05A18, 60C05, 60E15, 05C65
Mots-clés : partition lattice, hypergraphs, network reliability, cumulants, inclusion-exclusion principle 
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     author = {Klaus Dohmen and Peter Tittmann},
     title = {Bonferroni-Galambos inequalities for partition lattices},
     journal = {The electronic journal of combinatorics},
     year = {2004},
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     number = {1},
     doi = {10.37236/1838},
     zbl = {1062.05015},
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Klaus Dohmen; Peter Tittmann. Bonferroni-Galambos inequalities for partition lattices. The electronic journal of combinatorics, Tome 11 (2004) no. 1. doi: 10.37236/1838

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